Results seem sensible

Makefile

@@ -1,8 +1,8 @@
 HEADERS=weyl.h thickenings.h queue.h bitvec.h
 
-SPECIAL_OPTIONS=-O0 -g
+#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
 #SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
-#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
+SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
 
 OPTIONS=-m64 -march=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
 

bitvec.h

@@ -107,6 +107,14 @@ static inline void bv_intersection(const bitvec_t *x, const bitvec_t *y, bitvec_
   }
 }
 
+static inline void bv_difference(const bitvec_t *x, const bitvec_t *y, bitvec_t *result)
+{
+  int i;
+  for (i=0; i < BV_QWORD_RANK; i++) {
+    result->v[i] = x->v[i] & ~y->v[i];
+  }
+}
+
 static inline int bv_disjoint(const bitvec_t *x, const bitvec_t *y)
 {
   for(int i = 0; i < BV_QWORD_RANK; i++)

generate.c

@@ -5,15 +5,132 @@
 #include <strings.h>
 #include <stdio.h>
 
+char stringbuffer[100];
+char stringbuffer2[100];
+
+typedef struct {
+  node_t *graph;
+  int cosets;
+  int rank;
+  int order;
+  int hyperplanes;
+  semisimple_type_t type;
+  unsigned long left_invariance;
+  unsigned long right_invariance;
+  const char *alphabet;
+  int *buffer;
+} info_t;
+
+int shorten(int i, unsigned long left, unsigned long right, node_t *graph, int rank)
+{
+  int other, shorter = i;
+  do {
+    i = shorter;
+    for(int j = 0; j < rank; j++) {
+      other = graph[shorter].left[j];
+      if(left & (1 << j) &&
+	 graph[other].wordlength < graph[shorter].wordlength)
+	shorter = other;
+      other = graph[shorter].right[j];
+      if(right & (1 << j) &&
+	 graph[other].wordlength < graph[shorter].wordlength)
+	shorter = other;
+    }
+  } while(shorter != i);
+
+  return shorter;
+}
+
 void balanced_thickening_callback(const bitvec_t *pos, int size, void *data)
 {
   static long totcount = 0;
 
+  if(data) {
+    info_t *info = (info_t*)data;
+
+    unsigned long right_invariance = FIRSTBITS(info->rank);
+    unsigned long left_invariance = FIRSTBITS(info->rank);
+
+    int bit1, bit2left, bit2right, left, right;
+
+    for(int i = 0; i < size; i++) {
+      bit1 = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
+      for(int j = 0; j < info->rank; j++) {
+	left = info->graph[i].left[j];
+	right = info->graph[i].right[j];
+	bit2left = left < size/2 ? bv_get_bit(pos, left) : !bv_get_bit(pos, size - 1 - left);
+	bit2right = right < size/2 ? bv_get_bit(pos, right) : !bv_get_bit(pos, size - 1 - right);
+	if(bit1 != bit2left)
+	  left_invariance &= ~BIT(j);
+	if(bit1 != bit2right)
+	  right_invariance &= ~BIT(j);
+      }
+    }
+
+    printf("left: ");
+    for(int j = 0; j < info->rank; j++)
+      printf("%c", left_invariance & (1 << j) ? info->alphabet[j] : ' ');
+    printf(" right: ");
+    for(int j = 0; j < info->rank; j++)
+      printf("%c", right_invariance & (1 << j) ? info->alphabet[j] : ' ');
+
+    if(info->buffer) {
+      printf(" generators:");
+      queue_t queue;
+      int current, left, right, shortest;
+      int *buffer = info->buffer;
+
+      for(int i = 0; i < size/2; i++) {
+	buffer[i] = bv_get_bit(pos, i);
+	buffer[size-1-i] = !buffer[i];
+      }
+      for(int i = size-1; i >= 0; i--) {
+	if(buffer[i]) {
+	  int shortest = shorten(i, left_invariance, right_invariance, info->graph, info-> rank);
+	  printf(" %s", alphabetize(info->graph[shortest].word,
+				    info->graph[shortest].wordlength,
+				    info->alphabet,
+				    stringbuffer));
+	  buffer[i] = 0;
+	  queue_init(&queue);
+	  queue_put(&queue, i);
+	  while((current = queue_get(&queue)) != -1) {
+	    for(edgelist_t *edge = info->graph[current].bruhat_lower; edge != (edgelist_t*)0; edge = edge->next) {
+	      if(buffer[edge->to]) {
+		buffer[edge->to] = 0;
+		queue_put(&queue, edge->to);
+	      }
+	    }
+	    for(int j = 0; j < info->rank; j++) {
+	      left = info->graph[current].left[j];
+	      if(left_invariance & (1 << j) &&
+		 info->graph[left].wordlength < info->graph[current].wordlength &&
+		 buffer[left]) {
+		buffer[left] = 0;
+		queue_put(&queue, left);
+	      }
+	      right = info->graph[current].left[j];
+	      if(right_invariance & (1 << j) &&
+		 info->graph[right].wordlength < info->graph[current].wordlength &&
+		 buffer[right]) {
+		buffer[right] = 0;
+		queue_put(&queue, right);
+	      }
+	    }
+	  }
+	}
+      }
+    }
+
+    printf("\n");
+  }
+
+  /*
   if((++totcount) % 100000000 == 0) {
     fprintf(stderr, "Found balanced ideal: ");
     bv_print(stderr, pos, size/2);
     fprintf(stderr, "\n");
-  }
+    } */
 }
 
 int main(int argc, const char *argv[])
@@ -57,8 +174,6 @@ int main(int argc, const char *argv[])
 	right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
   }
 
-  ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
-
   // generate graph
 
   graph = graph_alloc(type);
@@ -68,48 +183,123 @@ int main(int argc, const char *argv[])
 
   // print stuff
 
+  int output_level = 2;
+  if(getenv("OUTPUT_LEVEL"))
+    output_level = atoi(getenv("OUTPUT_LEVEL"));
+
   rank = weyl_rank(type);                // number of simple roots
   order = weyl_order(type);              // number of Weyl group elements
   hyperplanes = weyl_hyperplanes(type);  // number of positive roots
 
-  fprintf(stderr, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n", rank, order, hyperplanes, cosets);
+  if(output_level >= 1) {
-  fprintf(stderr, "\n");
+    printf("Poset: ");
+    if(left_invariance) {
+      printf("<");
+      for(int j = 0; j < rank; j++)
+	if(left_invariance & BIT(j))
+	  fputc(alphabet[j], stdout);
+      printf("> \\ ");
+    }
 
-  /*
+    for(int i = 0; i < type.n; i++)
-  fprintf(stderr, "Shortest coset representatives: \n");
+      printf("%s%c%d", i == 0 ? "" : " x ", type.factors[i].series, type.factors[i].rank);
-  for(int i = 0, wl = 0; i < cosets; i++) {
+
-    if(i == 0) {
+    if(right_invariance) {
-      fprintf(stderr, "1");
+      printf(" / <");
-    } else if(graph[i].wordlength > wl) {
+      for(int j = 0; j < rank; j++)
-      fprintf(stderr, "\n%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+	if(right_invariance & BIT(j))
-      wl = graph[i].wordlength;
+	  fputc(alphabet[j], stdout);
-    } else
+      printf(">");
-      fprintf(stderr, "%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+    }
+    fprintf(stdout, "\n");
+
+    fprintf(stdout, "Rank: %d\tOrder: %d\tPositive Roots: %d\tCosets: %d\n\n", rank, order, hyperplanes, cosets);
+  }
+
+  if(output_level >= 3) {
+    fprintf(stdout, "Shortest coset representatives: \n");
+    for(int i = 0, wl = 0; i < cosets; i++) {
+      if(i == 0) {
+	fprintf(stdout, "1");
+      } else if(graph[i].wordlength > wl) {
+	fprintf(stdout, "\n%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+	wl = graph[i].wordlength;
+      } else
+	fprintf(stdout, "%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+    }
+    fprintf(stdout, "\n\n");
+  }
+
+  if(output_level >= 4) {
+    edgelist_t *edge;
+    fprintf(stdout, "Bruhat order in graphviz format:\n");
+    fprintf(stdout, "digraph test123 {\n");
+    for(int i = 0; i < cosets; i++) {
+      edge = graph[i].bruhat_lower;
+      while(edge) {
+	fprintf(stdout, "%s -> %s;\n",
+		alphabetize(graph[i].word, graph[i].wordlength, alphabet, stringbuffer),
+		alphabetize(graph[edge->to].word, graph[edge->to].wordlength, alphabet, stringbuffer2));
+
+	edge = edge->next;
+      }
+    }
+    fprintf(stdout, "}\n\n");
+  }
+
+  if(output_level >= 4) {
+    fprintf(stdout, "Opposites:\n");
+    for(int i = 0; i < cosets; i++) {
+      fprintf(stdout, "%s <-> %s\n",
+	      alphabetize(graph[i].word, graph[i].wordlength, alphabet, stringbuffer),
+	      alphabetize(graph[graph[i].opposite].word, graph[graph[i].opposite].wordlength, alphabet, stringbuffer2));
+
+    }
+    fprintf(stdout, "\n");
   }
-  fprintf(stderr, "\n\n");
-  */
 
   fixpoints = 0;
   for(int i = 0; i < cosets; i++)
     if(graph[i].opposite == i) {
-      if(fixpoints == 0)
+      if(output_level >= 1) {
-	fprintf(stderr, "No thickenings since the longest element fixes the following cosets: %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+	if(fixpoints == 0)
-      else
+	  fprintf(stdout, "No thickenings since the longest element fixes the following cosets: %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
-	fprintf(stderr, " %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+	else
+	  fprintf(stdout, " %s", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
+      }
       fixpoints++;
     }
+  if(output_level >= 1 && fixpoints)
+    fprintf(stdout, "\n\n");
 
-  if(fixpoints > 0) {
-    fprintf(stderr, "\n\n");
-  } else {
-    fwrite(&type.n, sizeof(int), 1, stdout);
-    fwrite(type.factors, sizeof(simple_type_t), type.n, stdout);
-    fwrite(&left_invariance, sizeof(unsigned long), type.n, stdout);
-    fwrite(&right_invariance, sizeof(unsigned long), type.n, stdout);
 
-    long count = enumerate_balanced_thickenings(graph, cosets, balanced_thickening_callback, (void*)0);
+  if(!fixpoints) {
+    int *buffer = (int*)malloc(cosets*sizeof(int));
 
-    fprintf(stderr, "Found %ld balanced thickenings\n\n", count);
+    info_t info;
+    info.graph = graph;
+    info.cosets = cosets;
+    info.rank = rank;
+    info.order = order;
+    info.hyperplanes = hyperplanes;
+    info.type = type;
+    info.left_invariance = left_invariance;
+    info.right_invariance = right_invariance;
+    info.alphabet = alphabet;
+    info.buffer = buffer;
+
+    long count;
+    if(output_level >= 2) {
+      fprintf(stdout, "Balanced ideals:\n", count);
+      count = enumerate_balanced_thickenings(graph, cosets, balanced_thickening_callback, &info);
+      fprintf(stdout, "\n", count);
+    }
+    else
+      count = enumerate_balanced_thickenings(graph, cosets, 0, 0);
+
+
+    if(output_level >= 1)
+      fprintf(stdout, "Found %ld balanced ideal%s\n", count, count == 1 ? "" : "s");
   }
 
   graph_free(type, graph);

queue.h

@@ -7,6 +7,11 @@
 #define QUEUE_SIZE 5000
 
 #define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
+#ifdef _DEBUG
+#define LOG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
+#else
+#define LOG(msg, ...)
+#endif
 
 typedef struct {
   unsigned int start;

thickenings.c

@@ -91,12 +91,10 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     graph[i].is_hyperplane_reflection = 0;
   }
 
-  // get coxeter graph
+  LOG("Generate Weyl group.\n");
 
   weyl_generate(type, graph_data);
 
-  fprintf(stderr, "Weyl group generated.\n");
-
   for(int i = 0; i < order; i++)
     for(int j = 0; j < rank; j++) {
       graph_unsorted[i].left = graph_data[i].left;
@@ -105,6 +103,8 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
 
   // find wordlengths
 
+  LOG("Determine word lengths.\n");
+
   graph_unsorted[0].wordlength = 0;
   queue_init(&queue);
   queue_put(&queue, 0);
@@ -118,9 +118,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Wordlengths calculated.\n");
+  LOG("Sort by wordlength.\n");
-
-  // sort by wordlength
 
   for(int i = 0; i < order; i++)
     ordering[i] = i;
@@ -135,9 +133,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
       graph[i].left[j] = reverse_ordering[graph_unsorted[ordering[i]].left[j]]; // rewrite references
   }
 
-  fprintf(stderr, "Sorted by wordlength.\n");
+  LOG("Find shortest words.\n");
-
-  // find words
 
   for(int i = 0; i < order; i++)
     memset(graph[i].word, 0, hyperplanes*sizeof(int));
@@ -154,9 +150,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Shortest words found.\n");
+  LOG("Generate right edges.\n");
-
-  // generate right edges
 
   for(int i = 0; i < order; i++) {
     for(int j = 0; j < rank; j++) {
@@ -168,9 +162,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Right edges generated.\n");
+  LOG("Find opposites.\n");
-
-  // find opposites
 
   node_t *longest = &graph[order-1];
   for(int i = 0; i < order; i++) {
@@ -180,9 +172,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     graph[i].opposite = current;
   }
 
-  fprintf(stderr, "Opposites found.\n");
+  LOG("Enumerate hyperplanes.\n");
-
-  // enumerate hyperplanes
 
   hyperplane_count = 0;
   for(int i = 0; i < order; i++) {
@@ -203,9 +193,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Hyperplanes enumerated.\n");
+  LOG("Determine Bruhat order.\n");
-
-  // generate folding order
 
   edgelist_count = 0;
   for(int i = 0; i < order; i++) {
@@ -229,9 +217,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Bruhat order generated.\n");
+  LOG("Perform transitive reduction.\n");
-
-  // remove redundant edges
 
   for(int i = 0; i < order; i++) {
     memset(seen, 0, order*sizeof(int));
@@ -272,9 +258,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Redundant edges removed.\n");
+  LOG("Revert Bruhat order.\n");
-
-  // reverse folding order
 
   edgelist_count = 0;
   for(int i = 0; i < order; i++) {
@@ -288,7 +272,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph)
     }
   }
 
-  fprintf(stderr, "Bruhat order reversed.\n");
+  LOG("Sort opposites.\n");
 
   // additional sorting step to force opposite property (opposite of j is at n - j - 1)
 
@@ -373,7 +357,7 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
   full_graph = graph_alloc(type);
   prepare_graph(type, full_graph);
 
-  fprintf(stderr, "Full graph generated.\n");
+  LOG("Full graph generated.\n");
 
   // initialize stuff
 
@@ -385,6 +369,8 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
     reduced[i] = i;
   }
 
+  LOG("Group by double coset.\n");
+
   // step 1: group
   for(int i = 0; i < order; i++) {
     if(group[i] != -1)
@@ -406,6 +392,8 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
     }
   }
 
+  LOG("Find minimal length elements.\n");
+
   // step 2: find minimum
   for(int i = 0; i < order; i++)
     if(full_graph[i].wordlength < full_graph[reduced[group[i]]].wordlength)
@@ -424,12 +412,11 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
   for(int i = 0; i < order; i++)
     simplified[i] = simplified[reduced[i]];
 
-  //  fprintf(stderr, "Number of double cosets: %d\n\n", ncosets);
-
-  //  simplified_graph = (node_t*) malloc(ncosets*sizeof(node_t));
   seen = (int*) malloc(ncosets*sizeof(int));
   edgelists_used = 0;
 
+  LOG("Copy minimal elements.\n");
+
   // step 5: set up nodes from minima
   current = 0;
   for(int i = 0; i < order; i++)
@@ -445,6 +432,8 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
       }
     }
 
+  LOG("Find induced order.\n");
+
   // step 6: find order relations
   for(int i = 0; i < order; i++) {
     edge = full_graph[i].bruhat_lower;
@@ -461,6 +450,8 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
     }
   }
 
+  LOG("Perform transitive reduction.\n");
+
   // step 7: remove redundant edges
   for(int i = 0; i < ncosets; i++) {
     memset(seen, 0, ncosets*sizeof(int));
@@ -477,7 +468,6 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
 	  previous = edge;
 	} else if(seen[edge->to]) {
 	  // this edge is redundant, remove it
-	  //	  fprintf(stderr, "removing edge from %d to %d\n", i, edge->to);
 	  if(previous)
 	    previous->next = edge->next;
 	  else
@@ -505,6 +495,8 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
     }
   }
 
+  LOG("Revert order.\n");
+
   // step 8: revert order
   edgelists_used = 0;
   for(int i = 0; i < ncosets; i++) {
@@ -517,33 +509,57 @@ int prepare_simplified_graph(semisimple_type_t type, unsigned long left, unsigne
     }
   }
 
-  // output as graphviz dot file
+  LOG("Sort opposites.\n");
-  /*
-  fprintf(stdout, "difull_graph test123 {\n");
-  for(int i = 0; i < ncosets; i++) {
-    edge = simplified_graph[i].bruhat_lower;
-    while(edge) {
-      fprintf(stdout, "%s -> %s;\n",
-      	     alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer),
-	     alphabetize(simplified_graph[edge->to].word, simplified_graph[edge->to].wordlength, alphabet, buffer2));
 
-      edge = edge->next;
+  int *ordering = (int*)malloc(ncosets*sizeof(int));
+  int *reverse_ordering = (int*)malloc(ncosets*sizeof(int));
+  node_t *unsorted = (node_t*)malloc(ncosets*sizeof(node_t));
+  int opp, pos;
+
+  pos = 0;
+  for(int i = 0; i < ncosets; i++) {  // first all the pairs
+    opp = simplified_graph[i].opposite;
+    if(opp > i) { // first occurrence of this pair
+      ordering[pos] = i;
+      ordering[ncosets-1-pos] = opp;
+      reverse_ordering[i] = pos;
+      reverse_ordering[opp] = ncosets-1-pos;
+      pos++;
     }
   }
-  fprintf(stdout, "}\n"); */
+  for(int i = 0; i < ncosets; i++)  // and finally the self-opposites
+    if(simplified_graph[i].opposite == i) {
+      ordering[pos] = i;
+      reverse_ordering[i] = pos;
+      pos++;
+    }
 
-  // some output
+  // now really do it
-  /*  for(int i = 0; i < ncosets; i++)
+  memcpy(unsorted, simplified_graph, ncosets*sizeof(node_t));
-      fprintf(stderr, "%s <=> %s\n", simplified_graph[i].wordlength == 0 ? "1" : alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer), simplified_graph[simplified_graph[i].opposite].wordlength == 0 ? "1" : alphabetize(simplified_graph[simplified_graph[i].opposite].word, simplified_graph[simplified_graph[i].opposite].wordlength, alphabet, buffer2)); */
+  for(int i = 0; i < ncosets; i++) {
-
+    simplified_graph[i] = unsorted[ordering[i]];
-  //  fprintf(stderr, "\nAdded %d edges.\n\n", edgelists_used);
+    simplified_graph[i].opposite = reverse_ordering[simplified_graph[i].opposite];
+    for(edgelist_t *edge = simplified_graph[i].bruhat_lower; edge != (edgelist_t*)0; edge = edge->next)
+      edge->to = reverse_ordering[edge->to];
+    for(edgelist_t *edge = simplified_graph[i].bruhat_higher; edge != (edgelist_t*)0; edge = edge->next)
+      edge->to = reverse_ordering[edge->to];
+    for(int j = 0; j < rank; j++) {
+      simplified_graph[i].left[j] = reverse_ordering[simplified_graph[i].left[j]];
+      simplified_graph[i].right[j] = reverse_ordering[simplified_graph[i].right[j]];
+    }
+  }
 
+  free(ordering);
+  free(reverse_ordering);
+  free(unsorted);
   free(seen);
   free(reduced);
   free(group);
   free(simplified);
   graph_free(type, full_graph);
 
+  LOG("Simplified graph generated.\n");
+
   return ncosets;
 }
 
@@ -637,6 +653,11 @@ static long enumerate_tree(const enumeration_info_t *info, const bitvec_t *pos,
   // everything before next_neg which was unknown should be set to positive; to speed this up, we can start with already_known
   bv_set_range_except(&newpos, neg, already_known, next_neg);
 
+  #ifdef _DEBUG
+  bv_print_nice(stderr, &newpos, &newneg, -1, info->size/2);
+  fprintf(stderr, "\n");
+  #endif
+
   // check if this leads to any conflicts (equivalently, violates slimness)
   if(!bv_disjoint(&newpos, &newneg))
     return 0;
@@ -728,12 +749,15 @@ long enumerate_balanced_thickenings(node_t *graph, int size, void (*callback) (c
   }
   free(principal);
 
-  /*
+  // output principal ideals
+#ifdef _DEBUG
   for(int i = 0; i < info.size; i++) {
-    fprintf(stderr, "%d: ", i);
+    fprintf(stderr, "%2d: ", i);
     bv_print_nice(stderr, &info.principal_pos[i], &info.principal_neg[i], -1, info.size/2);
     fprintf(stderr, "\n");
-    } */
+  }
+  fprintf(stderr,"\n");
+#endif
 
   // enumerate balanced ideals
   bitvec_t pos, neg;

weyl.c

@@ -283,10 +283,10 @@ void weyl_cartan_matrix(semisimple_type_t type, int *m)
       }
       break;
 
-    case 'B':          // not sure at all about the order of B and C
+    case 'B':        // not sure at all about the order of B and C
       if(type.factors[k].rank >= 2) {
-	A[0][1] = -1;
+	A[0][1] = -2;
-	A[1][0] = -2;
+	A[1][0] = -1;
       }
       for(int i = 2; i < type.factors[k].rank; i++) {
 	A[i][i-1] = -1;
@@ -296,8 +296,8 @@ void weyl_cartan_matrix(semisimple_type_t type, int *m)
 
     case 'C':
       if(type.factors[k].rank >= 2) {
-	A[0][1] = -2;
+	A[0][1] = -1;
-	A[1][0] = -1;
+	A[1][0] = -2;
       }
       for(int i = 2; i < type.factors[k].rank; i++) {
 	A[i][i-1] = -1;